Theoretical Study on Superconductor Properties for Penrose Lattices

Superconductivity in quasicrystal has been discovered in experiments [1] for Al–Zn–Mg quasicrystal with T_c ≈ 0.05 K. In this presentation, we sytematically studied the quasicrastal superconductor properties on Penrose lattices. Within two-particle approximation the negtive U Hubbard model shows that the Cooper binding ernergy is proportional to exp(-1/U) and Anderson Law works well. Besides, the negtive U Hubbard model was studied by the mean-field method with which the superconductor gap, superconductor density of states, entropy, specific heat, and current density are analyzed. The superconductor gap decreases to zero when the temperature is larger than T_c, simultaneously the lines entropy and specific heat show the superconductor phase by their discontinuities. The paramagnetic and diamagnetic superconductor currents also have discontinuities at T_c and cancel each other when T>Tc. Different from periodical lattices the superconductor current has a finite value when T = 0, which shows the difference of the superconductor behavior between the quasicrystals and common crystals.

[1] K. Kamiya, T. Takeuchi, N. Kabeya, N. Wada, T. Ishimasa, A. Ochiai, K. Deguchi, K. Imura, and N. K. Sato. Nature Communications 9, 154 (2018)